Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Log motivic exceptional direct image functors

Doosung Park

Abstract

In this paper, we construct the motivic exceptional direct image functors for fs log schemes. This construction is a part of the motivic six-functor formalism for fs log schemes.

Log motivic exceptional direct image functors

Abstract

In this paper, we construct the motivic exceptional direct image functors for fs log schemes. This construction is a part of the motivic six-functor formalism for fs log schemes.
Paper Structure (17 sections, 60 theorems, 138 equations)

This paper contains 17 sections, 60 theorems, 138 equations.

Table of Contents

  1. Introduction
  2. Log motivic infinity categories
  3. Support property
  4. Exact log smooth motives
  5. Log motivic infinity categories
  6. Modules
  7. Restrictions to exact log smooth log schemes
  8. Properties of exact log smooth motives
  9. Strict smooth motives
  10. Support property
  11. Basic properties of the support property
  12. Strictly universal support property
  13. Projection formula
  14. Support property for some vertical morphisms
  15. Support property for some non-vertical morphisms
  16. ...and 2 more sections

Key Result

Theorem 1.1.1

let $\mathbb{E}$ be a commutative algebra object of $\mathcal{SH}(B)$. Then $\mathcal{SH}$ and $\mathrm{Mod}_{\mathbb{E}}$ are log motivic $\infty$-categories.

Theorems & Definitions (125)

  • Theorem 1.1.1: Theorems \ref{['restriction.15']} and \ref{['logChow.8']}
  • Theorem 1.2.1: Theorem \ref{['nonversupp.13']}
  • Theorem 1.2.2
  • Definition 2.1.1
  • Theorem 2.1.2
  • proof
  • Lemma 2.2.4
  • proof
  • Theorem 2.2.6
  • proof
  • ...and 115 more